Frequency shifts in emission and absorption by resonant systems ot two-level atoms

Physical properties of dense, low-temperature plasmas

A theory is given for the rotational band contours in microwave, infrared, and Raman spectra, and for nuclear spin—lattice relaxation times. The results are a generalization of Baranger's impact calculation for atomic spectra. The semiclassical approach makes possible nonperturbative calculations beginning directly from the intermolecular potential. When the rotational lines are well resolved, the results reduce to our previous semiclassical expressions for the widths and shifts of isolated rotational lines. At higher densities the results describe the ``collapse'' or narrowing of the band contour which happens when the rotational lines overlap.

Semiclassical Theory of Spectra and Relaxation in Molecular Gases

Spectral Line Shapes in Gases in the Binary‐Collision Approximation

The problem of the pressure broadening of spectral lines is investigated with respect to the microwave absorption of two terrestrial atmospheric gases, oxygen and water vapor. A formalism and accompanying computational procedures under the impact approximation and using the Liouville (line) Space concept introduced by Baranger and elaborated by Fano are employed. It is desired that the theory would obviate the necessity for specific line shapes, provide a means of computing line widths and account for line overlapping effects from first principles. The present approach is found to be generally adequate for the treatment of O2 absorption on comparison with experimental data for line widths, absorption coefficients and zenity opacities. While H2O line widths are satisfactorily predicted, estimated resonance overlapping effects are found to be far from sufficient (accounting for at most ~ 5%) to explain the theoretically controversial anomalous absorption.

Application of pressure broadening theory to the calculation of atmospheric oxygen and water vapor microwave absorption

Pressure broadening as a many-body problem☆☆☆

The stability of a weakly ionized plasma in a strong electric field against the formation of longitudinal waves is investigated theoretically in the hydrodynamic limit $\mathrm{ql}\ensuremath{\ll}1$ where $q$ is the wave number, and $l$ is a relaxation length related to the mean free paths of the charge carriers. Applications of the theory to semiconductors and gases are considered. The behavior of the charge carriers in response to slowly varying disturbances is dominated by their collisions with the lattice or the neutral atoms, implying that an approximate equilibrium is maintained between the local field and the local densities, drift velocities, and effective temperatures of the carriers. The mean thermal energy or effective temperature of the electrons in the steady state depends on the magnitude of the applied field and can be much greater than the lattice or neutral-atom temperature. In general, this means that the electron mobility is also field-dependent. It is shown that this field dependence and the local equilibrium condition can lead to temperature oscillations which affect the phase velocity and damping of excitations resembling ion-acoustic waves. It is predicted that when the applied field exceeds a critical value the damping constant will change sign, and the system will become unstable. The feasibility of detecting this instability is discussed, and comparisons with other instabilities are made.

Oscillations of a Weakly Ionized Plasma in a Strong Electric Field

Hydrodynamic equations describing the motion of electrons in a weakly ionized plasma are derived formally from the Boltzmann equation by means of the Chapman-Enskog procedure. Two cases are considered, each with a stationary Maxwellian distribution ascribed to the atoms. In the first, electron-electron collisions are ignored, and the electron distribution function is determined by a balance between the electron-atom collisions and the electric field. There is only one conservation law, a hydrodynamic equation for the density. In the second case, electron-electron collisions are dominant, the distribution function is a local Maxwellian, and there are five conservation laws---equations for the density, drift velocity, and temperature. The equations used previously by the author to describe low-frequency oscillations are obtained in either case if the electron-atom collision frequency is independent of velocity. Otherwise, the zeroth-order equations are still exact, but first-order corrections are required, as illustrated by the example of the velocity-independent mean free path. Our results are somewhat different from those of Davidov, who made different assumptions about the dominant collision mechanisms.

David W. Ross

Papers

Pressure broadening as a many-body problem☆☆☆

Oscillations of a Weakly Ionized Plasma in a Strong Electric Field

Comments on the Solution to the Boltzmann Equation for a Weakly Ionized Plasma